Al-Jabr

Al-jabr is the Arabic term for algebra, derived from a word for restoring or reuniting. In al-Khwarizmi’s method, it names the operation that removes a subtracted quantity by adding it to both sides of an equation.

Al-Muqabala: An operation in early algebra that cancels equal positive terms from both sides of an equation. It is al-jabr’s companion operation: after restoring a subtracted term, al-muqabala simplifies matching terms.
Al-Khwarizmi: A ninth-century Persian mathematician whose works helped establish algebra as a systematic discipline. His book named al-jabr and made the operation central to its equation-solving method.
Robert of Chester: A twelfth-century English translator who rendered al-Khwarizmi’s algebra treatise into Latin. His Latin translation helped transmit the word and methods associated with al-jabr.
Etymology of algebra: The linguistic history of the word algebra, traced through Arabic al-jabr and its Latin transmission. The word’s history centers on al-jabr’s meaning of restoration or rejoining.
Linear equation: An equation in which the unknown appears only to the first power. Al-Khwarizmi demonstrated al-jabr by reducing linear equations to standard forms.
The Compendious Book on Calculation by Completion and Balancing: Al-Khwarizmi’s ninth-century Arabic treatise presenting methods for solving linear and quadratic equations. Its title translates al-jabr wa’l-muqabala, preserving the paired operations behind the term.
Algorism: A medieval term for arithmetic performed by the Hindu-Arabic numeral system, derived from al-Khwarizmi’s name. Algorism and algebra preserve different legacies of al-Khwarizmi’s mathematical work.
Arabic language: A Semitic language with a long written tradition across the Middle East and North Africa. Al-jabr’s original meaning and grammatical form belong to Arabic.
Quadratic equation: An equation whose highest-power term in the unknown is squared. Al-Khwarizmi’s treatment of quadratic equations shows al-jabr working beyond first-degree problems.
Arabic mathematics: Mathematical scholarship written in Arabic across the medieval Islamic world and beyond. Al-jabr entered mathematical vocabulary through this multilingual scholarly tradition.

Linked from 2 pages